The mechanism of the adsorption and grafting of diazonium cations onto the surface of graphyne and graphdiyne was investigated using Density Functional Theory (DFT). The adsorption energy (both in vacuum and water as solvent) of the phenyl diazonium cation was evaluated at three different positions of the graphyne and graphdiyne surface. Moreover, the lowest energy adsorption sites were used to calculate and plot Non-covalent Interactions (NCI). The Bond Dissociation Energy (BDE) results (up to 66 kcal/mol) for the scission of the phenyl group support the remarkable stability of the grafted layer. As both of these materials are non-dispersible in aqueous solution, in this work through the use of Molecular Mechanics (MM) and Molecular Dynamics (MD) we explored also the effect of the grafted substituted aryl groups derived from aryldiazonium salts onto the solvation properties of these materials.